idamnjanovic@1: function [dist,ratio] = dictdist(approxD,D,epsilon)
idamnjanovic@1: %DICTDIST Distance between dictionaries.
idamnjanovic@1: %  [DIST,RATIO] = DICTDIST(APPROXD,D) computes the distance between the
idamnjanovic@1: %  approximate dictionary APPROXD and the true dictionary D, where APPROXD
idamnjanovic@1: %  is NxK and D is NxM.
idamnjanovic@1: %
idamnjanovic@1: %  The distance between the dictionary APPROXD and a single atom A of D is
idamnjanovic@1: %  defined as:
idamnjanovic@1: %
idamnjanovic@1: %      DIST(APPROXD,A) = min  { 1-abs(APPROXD(:,i)' * A) }
idamnjanovic@1: %                         i
idamnjanovic@1: %
idamnjanovic@1: %  The distance between the dictionaries APPROXD and D is defined as:
idamnjanovic@1: %
idamnjanovic@1: %      DIST(APPROXD,D) = sum { dist(APPROXD, D(:,k)) } / M
idamnjanovic@1: %                         k
idamnjanovic@1: %
idamnjanovic@1: %  Note that 0 <= DIST(APPROXD,D) <= 1, where 0 implies that all atoms in D
idamnjanovic@1: %  appear in APPROXD, and 1 implies that the atoms of D are orthogonal to
idamnjanovic@1: %  APPROXD.
idamnjanovic@1: %
idamnjanovic@1: %  The similarity ratio between APPROXD and D is defined as:
idamnjanovic@1: %
idamnjanovic@1: %      RATIO(APPROXD,D) = #(atoms in D that appear in APPROXD) / M
idamnjanovic@1: %
idamnjanovic@1: %  where two atoms are considered identical when DIST(A1,A2) < EPSILON with
idamnjanovic@1: %  EPSILON=0.01 by default. Note that 0 <= RATIO(APPROXD,D) <= 1, where 0
idamnjanovic@1: %  means APPROXD and D have no identical atoms, and 1 means that all atoms
idamnjanovic@1: %  of D appear in APPROXD.
idamnjanovic@1: %
idamnjanovic@1: %  [DIST,RATIO] = DICTDIST(DICT1,DICT2,EPSILON) specifies a different value
idamnjanovic@1: %  for EPSILON.
idamnjanovic@1: 
idamnjanovic@1: %  Ron Rubinstein
idamnjanovic@1: %  Computer Science Department
idamnjanovic@1: %  Technion, Haifa 32000 Israel
idamnjanovic@1: %  ronrubin@cs
idamnjanovic@1: %
idamnjanovic@1: %  October 2007
idamnjanovic@1: 
idamnjanovic@1: 
idamnjanovic@1: if (nargin < 3), epsilon = 0.01; end
idamnjanovic@1: 
idamnjanovic@1: [n,m] = size(D);
idamnjanovic@1: 
idamnjanovic@1: approxD = normcols(approxD*spdiag(sign(approxD(1,:))));
idamnjanovic@1: D = normcols(D*spdiag(sign(D(1,:))));
idamnjanovic@1: 
idamnjanovic@1: identical_atoms = 0;
idamnjanovic@1: dist = 0;
idamnjanovic@1: 
idamnjanovic@1: for i = 1:m
idamnjanovic@1:   atom = D(:,i);
idamnjanovic@1:   distances = 1-abs(atom'*approxD);
idamnjanovic@1:   mindist = min(distances);
idamnjanovic@1:   dist = dist + mindist;
idamnjanovic@1:   identical_atoms = identical_atoms + (mindist < epsilon);
idamnjanovic@1: end
idamnjanovic@1: 
idamnjanovic@1: dist = dist / m;
idamnjanovic@1: ratio = identical_atoms / m;